Optimal filtering over linear observations with unknown parameters

This paper presents the optimal filtering and parameter identification problem for linear stochastic systems over linear observations with unknown parameters, where the unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state...

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Bibliographic Details
Published in:Journal of the Franklin Institute 2010-08, Vol.347 (6), p.988-1000
Main Authors: Basin, Michael, Calderon-Alvarez, Dario
Format: Article
Language:English
Subjects:
Kalman filtering
Parameter identification
Uncertain linear stochastic system
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Summary:This paper presents the optimal filtering and parameter identification problem for linear stochastic systems over linear observations with unknown parameters, where the unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The resulting filtering system is bilinear in state and linear in observations. The obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed optimal state filter and parameter identifier is verified for both, positive and negative, parameter values.
ISSN:0016-0032
1879-2693
DOI:10.1016/j.jfranklin.2010.01.006